Fast Diffusion of Bound Ca: Analytical and Experimental Characterization of One- and Two-Dimensional Traveling Waves
- 1Georg-August-University
Abstract
Reaction–diffusion (RD) systems play a fundamental role in numerous biochemical and biophysical processes. Here, we present a novel analytical framework for solving RD equations by applying the Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) formalism to Ca 2+ buffering. Previous models have primarily focused on stationary Ca 2+ nanodomains while neglecting diffusion and saturation of intracellular Ca 2+ buffers and sensors. We derive analytical solutions using WKBJ ansatz and demonstrate that sustained Ca 2+ source produces continuously expanding distributions of free Ca 2+ , whereas the concentration of Ca 2+ -bound buffers develops at much slower timescale. These predictions are supported experimentally by measurements of one-dimensional fluorescence profiles produced by single-channel activity and two-dimensional profiles generated by whole-cell Ca 2+ currents. The analytical framework developed here extends Michaelis–Menten-type kinetics to reaction–diffusion systems and may therefore be broadly applicable to biochemical and biophysical processes in which diffusion cannot be neglected.
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BibTeX
@misc{mironov2026fast,
title = {{Fast Diffusion of Bound Ca: Analytical and Experimental Characterization of One- and Two-Dimensional Traveling Waves}},
author = {S. Mironov},
howpublished = {bioRxiv},
year = {2026},
month = jul,
doi = {10.64898/2026.07.06.735233},
url = {https://www.biorxiv.org/content/10.64898/2026.07.06.735233v2},
note = {Public domain},
}
RIS
TY - UNPB
TI - Fast Diffusion of Bound Ca: Analytical and Experimental Characterization of One- and Two-Dimensional Traveling Waves
AU - S. Mironov
PY - 2026
DA - 2026/07/06
PB - bioRxiv
DO - 10.64898/2026.07.06.735233
UR - https://www.biorxiv.org/content/10.64898/2026.07.06.735233v2
AB - Reaction–diffusion (RD) systems play a fundamental role in numerous biochemical and biophysical processes. Here, we present a novel analytical framework for solving RD equations by applying the Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) formalism to Ca 2+ buffering. Previous models have primarily focused on stationary Ca 2+ nanodomains while neglecting diffusion and saturation of intracellular Ca 2+ buffers and sensors. We derive analytical solutions using WKBJ ansatz and demonstrate that sustained Ca 2+ source produces continuously expanding distributions of free Ca 2+ , whereas the concentration of Ca 2+ -bound buffers develops at much slower timescale. These predictions are supported experimentally by measurements of one-dimensional fluorescence profiles produced by single-channel activity and two-dimensional profiles generated by whole-cell Ca 2+ currents. The analytical framework developed here extends Michaelis–Menten-type kinetics to reaction–diffusion systems and may therefore be broadly applicable to biochemical and biophysical processes in which diffusion cannot be neglected.
ER -